\(\sin 2\theta=2\sin\theta\cos\theta\)
\(\cos 2\theta=\cos^2\theta-\sin^2\theta=2\cos^2\theta-1=1-2\sin^2\theta\)
\(\tan 2\theta=\dfrac{2\tan\theta}{1-\tan^2\theta}\)

\(\sin 2\theta=\sin(\theta+\theta)\) \(=\sin\theta\cos\theta+\cos\theta\sin\theta=2\sin\theta\cos\theta\)

\(\cos 2\theta=\cos(\theta+\theta)\) \(=\cos\theta\cos\theta-\sin\theta\sin\theta=\cos^2\theta-\sin^2\theta\)
また，\(\cos^2\theta-\sin^2\theta=\cos^2\theta-(1-\cos^2\theta) =2\cos^2\theta-1\)
さらに，\(\cos^2\theta-\sin^2\theta=(1-\sin^2\theta)-\sin^2\theta =1-2\sin^2\theta\)

\(\tan 2\theta=\dfrac{\tan\theta+\tan\theta}{1-\tan\theta\tan\theta} =\dfrac{2\tan\theta}{1-\tan^2\theta}\)